Which of the following numbers is a multiple of 10? ${42,58,61,71,110}$
Answer: The multiples of $10$ are $10$ $20$ $30$ $40$ ..... In general, any number that leaves no remainder when divided by $10$ is considered a multiple of $10$ We can start by dividing each of our answer choices by $10$ $42 \div 10 = 4\text{ R }2$ $58 \div 10 = 5\text{ R }8$ $61 \div 10 = 6\text{ R }1$ $71 \div 10 = 7\text{ R }1$ $110 \div 10 = 11$ The only answer choice that leaves no remainder after the division is $110$ $ 11$ $10$ $110$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $10$ are contained within the prime factors of $110$ $110 = 2\times5\times11 10 = 2\times5$ Therefore the only multiple of $10$ out of our choices is $110$. We can say that $110$ is divisible by $10$.